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81.
ABSTRACTIn this paper, we introduce a discrete convolution involving both the Fourier sine and cosine series. We study Young's type inequality and a discrete transform related to this convolution and solve in closed form a class of discrete Toeplitz plus Hankel equations. 相似文献
82.
In this paper, we first introduce the concept of the ?-product on function space. We then proceed to use this concept to obtain several integration formulas. In addition, we establish various relationships which exist. Also, we establish the relationships among the ?-product, the generalized convolution product and the first variation. 相似文献
83.
84.
A linear operator associated with the Mittag-Leffer function and related conformal mappings 下载免费PDF全文
In the present paper, we introduce a linear operator associated with the Mittag-Leffler function. Some convolution properties of meromorphic functions involving this operator are given. 相似文献
85.
运用所给出的引理及离散的Fourier变换, 在$L_2[-\pi, \pi]$上讨论了一类具周期性的含卷积核与余割核$\csc(\tau-\theta)$混合的奇异积分方程,把此类方程转化为离散跃度问题, 得到了方程的可解条件和一般解的显式. 相似文献
86.
Ghislain R. Franssens 《Applicable analysis》2013,92(3):333-356
This is the second in a series of two papers in which we construct a convolution product for the set ?′ (R) of associated homogeneous distributions (AHDs) with support in R. In Part I we showed that if f a and g b are AHDs with degrees of homogeneity a ? 1 and b ? 1, the convolution f a * g b exists as an AHD, if the resulting degree of homogeneity a + b?1 ? N. In this article, we develop a functional extension process, based on the Hahn–Banach theorem, to give a meaning to the convolution product of two AHDs of degrees a ? 1 and b ? 1, in the critical case that a + b ? 1 ∈ N. With respect to this construction, the structure (?′(R), *) is shown to be closed. 相似文献
87.
T. Matsuura 《Applicable analysis》2013,92(8):901-915
We shall discuss the relations among sampling theory (Sinc method), reproducing kernels and the Tikhonov regularization. Here, we see the important difference of the Sobolev Hilbert spaces and the Paley–Wiener spaces when we use their reproducing kernel Hibert spaces as approximate spaces in the Tikhonov regularization. Further, by using the Paley–Wiener spaces, we shall illustrate numerical experiments for new inversion formulas for the Gaussian convolution as a much more powerful and improved method by using computers. In this article, we shall be able to give practical numerical and analytical inversion formulas for the Gaussian convolution that is realized by computers. 相似文献
88.
89.
Yoshishige Haraoka 《Journal of Nonlinear Mathematical Physics》2013,20(4):70-84
We extend the notion of deformation to inverse operations of restrictions of completely integrable systems to regular or singular locus, and call the extended notion prolongation. We show that a prolongability determines uniquely a Fuchsian ordinary differential equation of rank three with three regular singular points. This seems similar to that the deformation equation determines the accessory parameters as a function of the geometric moduli. Relations between prolongations and middle convolutions is also studied. 相似文献
90.
For k a commutative ring, H a k‐bialgebra and A a right H‐comodule k‐algebra, we define a new multiplication on the H‐comodule A to obtain a twisted algebra” AT, T sumHom(H,End (A)). If T is convolution invertible, the categories of relative right Hopf modules over A and ATare isomorphic. Similarly a convolution invertible left twisting gives an isomorphism of the categories of relative left Hopf modules. We show that crossed products are invertible twistings of the tensor product, and obtain, as a corollary, a duality theorem for crossed products 相似文献